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Question

1) Answer the following questions based on the \(P-T\) phase diagram of carbon dioxide:
A) At what temperature and pressure can the solid, liquid and vapour phases of \(CO_2\) co-exist in equilibrium?

2) Answer the following questions based on the \(P-T\) phase diagram of carbon dioxide:
B) What is the effect of decrease of pressure on the fusion and boiling point of \(CO_2\)?

3) Answer the following questions based on the \(P-T\) phase diagram of carbon dioxide:

C) What are the critical temperature and pressure for \(CO_2?\)
What is their significance?

4) Answer the following questions based on the \(P-T\) phase diagram of carbon dioxide:

D) Is \(CO_2\) solid, liquid or gas at \((a)-70^{\circ}C\) under \(1~\text{atm},(b)-60^{\circ}C\) under \(10\text{atm}~,(c)15^{\circ}C\) under \(56~\text{atm}?\)

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Solution

1) The \(P-T\) phase diagram for \(CO_2\) is shown in the following figure. \(C\) is the triple point of the \(CO_2\) phase diagram. This means that at the temperature and pressure corresponding to this point\((i.e.,\text{at}-56.6^{\circ}C~\text{and}5.11\text{atm}),\) the solid, liquid, and vaporous phases of \(CO_2\) co-exist in equilibrium.


2) The fusion and boliling point of \(CO_2\) decrease with a decrease in pressure as can be seen from the graph.


3) The critical temperature and critical pressure of \(CO_2~\text{are}~31.1^{\circ}C~\text{and}73\text{atm}\) respectively. If the temperature of carbon dioxide is more than \(31.1^{\circ}C,\) it can not be liquefied, however large pressure we may apply.

4) It can be seen from the \(P_T\) phase diagram of \(CO_2\) that:
(a) \(CO_2~\text{is gaseous at}-70^{\circ}C,~\text{under 1 atm pressure.}\)
(b) \(CO_2 \text{is solid at}-60^{\circ}C,~\text{under}10~atm\text{pressure.}\)
(c) \(CO_2\text{is liquid at}15^{\circ}C,\text{under}~56~atm~\text{pressure.}\)


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